Geodesic Tires are those tires whose ply cord paths are geodesic lines on the tire surface. John F Purdy, the author of Mathematics Underlying the Design of Pneumatic Tires, copyrighted in 1963, was the Chief Mathematician of the Development Department of The Goodyear Tire & Rubber Company and for 45 years he devoted his life to the mathematics underlying tire design. In Chapter IV of Mr Purdy's book, the entire subject matter discloses the principles of Geodesic tires. The author notes his interest in the geodesic cord path first occurred in 1917 as a student of mathematics. Experiments with geodesic tires first began about 1924.
Purdy discloses that a geodesic tire has many desirable features. Quoting Purdy at page 85 of the book "Its durability is excellent due to the absence of shear forces that in conventional tires result in a separation of rubber from fabric and that contribute to fabric fatigue through the torsion of the cords about their own axis during the shear cycle as the tire flexes. The absence of these same shear forces lower the operating temperature of a geodesic tire from the temperature of conventional tires. Improved durability in the vicinity of the tire bead results from the relatively small angle .alpha. at which the cords approach the bead. In many types of tire subject to large driving torque or to severe brake action, damaging torque buckles appear in the tire sidewalls. These are virtually absent in geodesic tires.
Due principally to the large cord angle over the crown, the geodesic tires provide a very soft ride at inflation pressures common to conventional tires of the same size. The same large cord angle over the crown reduces the lateral stability of the tire somewhat, and its ability to develop lateral thrust against the road when rounding a curve. This in itself might be a serious score against the geodesic tire if it were not for the fact that if inflation pressure is raised to the point where softness of ride approaches that of a conventional tire, lateral stability and cornering ability are as good or better than those of a conventional tire.
The geodesic path represents a long step forward in providing desirable properties in a tire that are possible for design alone to provide.
Geodesic tires have not become commonly known to users of tires largely because they require different procedures in the building of the tire than are required for the easily built conventional tires, and because of the fact that for normal purposes conventional tires are highly satisfactory products. The increasing range of conditions under which tires now operate demands new thinking in the art of design and tires of nonconventional cord path is one of the most important forward steps in meeting unusual requirements. Unfortunately the term geodesic has been flaunted in public in recent time with reference to tires that have no semblance whatever to geodesics. For the term geodesic is a mathematically precise term and a path or a curved surface departing only a little from a geodesic path easily loses the merits of geodesics. The failure to obtain a geodesic path in a tire is often the failure to understand some of the simple mechanics of tire construction.
Therefore, to obtain a given geodesic path in a tire, conventional building practice could be followed if the cord path in the flat ply were that path which pantographic action together with the effect of a prescribed tension would transform to a geodesic path on shaping from building form to mold.
The results of this reasoning have invariably been tires with perfect geodesic paths, conforming perfectly to the requirements that .rho.. cos .alpha.=a constant, .rho.o cos .alpha.o, that cord tension be uniform over the entire cord path, and that shear stresses due to inflation pressure be zero".
Purdy then goes on to describe numerous attempts to build experimental geodesic tires a brief excerpt of this background art is given starting at page 91.
"The earliest geodesic tires, and some for later experiment, were built by laying cords or groups of cords along a template whose shape was that of the necessary cord path in the flat ply.
The resulting tires were highly satisfactory for experiment. A number of machines have been subject to patent and operate to wind a continuous cord on a core not far different in shape from the finished tire. The same machines could wind a continuous cord in a geodesic path on a building drum. The simultaneous motion of the guide that feeds the cord onto the core and the turning of the core make it possible for the cord to be laid to any prescribed path. The difficulty in this process arises from two principal reasons. To wind a continuous cord back and forth over a building form requires either that the cord path approach the bead along a line tangent to the bead circle or else a sharp reversal of direction of the winding mechanism if the angle of the cord at the bead circle is greater than zero. In either case, the tension in the cords necessary for a satisfactory shaping and curing the tire is very difficult to attain. The continuous winding of a cord also involves an overlapping of successive winds in the region of the bead. This also involves poor tension control and the added problem of an unreasonably large bead bulk. An alternative is to continue the winding to some circle of radius less than that of the bead circle and then cut the cords at some P that will allow a turn of the ply around the bead. This last is not an economical procedure however.
Next in the line of planning non-conventional cord paths was the type of machine in which plies of fabric were used that had been prepared in the conventional manner, the cords of each ply lying in straight and parallel paths, the angle .beta. being the required .beta. at the center line of the ply that was to become a geodesic path ply in the tire. The edges of the ply were seized by rings rotating on the same axis as that of the building form, and that held the ply at first just off the drum. As rollers pressed the ply onto the building form beginning at the center-line of the ply and moved from center-line toward the edges of the ply, the rings in which the ply-edges were held rotated independently of the rotation of the drum and of each other and in a manner prescribed to alter the cord angle continuously as the roller pressed the plies onto the building form, with the result that the cords of the ply lay in paths on the drum surface that would become geodesic plies in the shaped tire. Such a procedure was, of course, not confined to geodesic path tires but could, by prescribed rotation of the building drum and the side rings lay any desired path on the drum."
A cord is limited in its effort to adjust its position to make its tension uniform due to the modulus of rigidity of the rubber around it; and a tension appropriate to move the cord to its shortest path is not the same tension for all increments. There is, therefore, at best, a very large difference between the irregular path assumed by the cord and a geodesic path between its terminal points. Repeated experiments over a long period of years have always been with the same unsatisfactory results.
Now suppose the plies of a tire were lubricated with some compound that would remain a very slippery medium between plies during the shaping process but would be absorbed during cure to permit a satisfactory adhesion between plies of the finished tire. After computing the conditions of cord angle, cord length, and radial angle .psi. most favorable to the formation of a geodesic path by adjustment of the tire cords over the slippery ply surfaces, several attempts were made to form geodesic paths. The lubricants used were first zinc stearate or stearic acid in liberal quantities. For still more slippery surfaces castor oil was used. Both rayon and nylon cords were used in the several experiments.
The most favorable conditions for success were the following. A geodesic path was selected for the tire and the length of the path and the radial angles subtended by the cord path were computed. To subtend the same radial angle .psi. on the building drum and the length of cord path differing from that in the tire only by an amount that would permit a reasonably large tension on shaping from core to mold, the width of the building drum and the bias angle of the ply were determined.
Purdy goes on to say at page 95 these ideal conditions for compelling a cord in a ply to seek a geodesic path in the tire, not one of numerous experiments came anywhere near the geodesic path. At tread center a difference of the order of 20.degree. existed between the path obtained and the geodesic. At the bead, the difference was of the order of 15.degree.. Furthermore the paths obtained were irregular and uncontrollable from time to time and from ply to ply. Not only are there sound theoretical reasons why the cords act as they do; the compelling fact is that experiment after experiment proves it to be true."
Rarely do the inventors of a new concept have such a wealth of background information regarding their invention. Purdy both explains the practical and theoretical value of geodesic tires. He goes on to explain that simple methods to achieve such a geodesic tire have reportedly met with failure primarily due to the inability to replicate the product.
Luigi Maiocchi, an Italian inventor, disclosed in U.S. Pat. No. 3,062,258 a tire having a central geodetic disposition of ply cords and two lateral portions including the bead and sidewall in which the cords form a substantially crossed structure.
To Purdy this hybrid tire would have been one of many misuses of the term "geodetical".
Nevertheless, Maiocchi did contribute an insight into the complexity of fabricating such a theoretically pure tire as a geodesic tire.
The present invention described hereinafter can be repeatedly built and tests indicated that the tire has achieved a consistent mimic of the geodesic plycord path from near the bead cores through the sidewall across the crown to the opposite bead cores. In one embodiment of the invention experimental race tires were built that survived durability testing over two hours at 239 mph, the tire being lighter in weight and substantially more durable than the prior art control tire.